The equation AX = BX implies $A^*X;=;B^X$ when A and B are normal (Fuglede-Putnam theorem). In this paper, the hypotheses on A and B can be relaxed by usin a Hilbert-Schmidt operator X: Let A be p-quasihyponormal and let $B^*$ be invertible p-quasihyponormal such that AX = XB for a Hilbert-Schmidt operator X and $|||A^*|^{1-p}||{cdot}|||B^{-1}|^{1-p}||;{leq};1$.Then $A^*X;=;XB^*$.